equation for parabola with focus (8,-2) directrix x=4

Answer 1

The standard parabola y^2 = 4px has focus at (p,0). So, we want to make that distance=4, so p=2.

That gives us y^2 = 8x for a parabola with focus at (8,0). Now shift that focus to (8,4) and we have

(y-4)^2 = 8x